Karnataka Board PUCPUC Science Class 11

Elastic Moduli - Young’s Modulus

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Notes

Elastic Modulus

  • Elastic modulus is the ratio of stress and strain.

  • Elastic modulus is a characteristic value of each material. This means gold will have a specific value of elastic modulus and rubber will have a specific value of elastic modulus etc.

  • `"k"="Stress"/"Strain"` Where k= Elastic modulus.

Types of elastic modulus:

1. Young’s Modulus:

Young’s modulus is derived from the name of the scientist who defined it.

  • It is the ratio of longitudinal stress to longitudinal strain.

  • It is denoted by Y.

  • Mathematically:

  • `"Y"= "longitudinal stress"/ "longitudinal strain" = σ/ ε`

  • `= ("F"/"A")/((Δ"L")/"L")`

  • `"Y"="FL"/(Δ"L")`

  • If Young’s modulus is more, to produce a small change in length more force required.

  • S.I. unit is `"Nm"^(–2)` or Pascal (Pa).

  • Metals have comparatively greater Young’s Modulus. To change the length of metals, greater force is required.

Young’s Modulus: Application

  • In industrial construction, steel is preferred over copper. The reason behind this is steel is more elastic than copper.

  • If there is slight deformation in steel due to contraction and expansion it will come back to its original position.

  • Steel is preferred over copper to construct bridges.

Substance

Density rho `("kgm"^-3)`

Youngs modulus Y `(10^9"Nm"^-2)`

Ultimate strength, `sigma_u(10^6"Nm"^-2)`

Yield strength `sigma_y(10^6"Nm"^-2)`

Aluminum

2710

70

110

95

Copper

8890

110

400

200

Iron (wrought)

7800-7900

190

330

170

Steel

7860

200

400

250

Glass

2190

65

50

-

Concrete

2320

30

40

-

Wood

525

13

50

-

Bone

1900

9.4

170

-

Polystyrene

1050

3

48

-

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